CAT 2022 Slot 3 QA Question 21: In a triangle ABC, $AB = AC = 8$ cm. A circle drawn with $BC$ as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area, in sq. cm, of the overlapping r

Question

In a triangle ABC, $AB = AC = 8$ cm. A circle drawn with $BC$ as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area, in sq. cm, of the overlapping r

Accepted Answer

Since the circle with $BC$ as diameter passes through A, angle $BAC$ is $90\degree$.
Given $AB = AC = 8$ cm, triangle ABC is an isosceles right triangle.
$BC = 8 \sqrt{2}$
The circle with BC as diameter has radius
$\dfrac{BC}{2} = 4 \sqrt{2}$
Area = $\pi(4 \sqrt{2})^2 = 32\pi$
The portion of this ci

In a triangle ABC, AB=AC=8AB = AC = 8AB=AC=8 cm. A circle drawn with BCBCBC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area, in sq. cm, of the overlapping region between the two circles is

In a triangle ABC, $AB = AC = 8$ cm. A circle drawn with $BC$ as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area, in sq. cm, of the overlapping region between the two circles is